Ok, I finally got around to playing it, and it was cool. I do have some things to criticize; I hope not to discourage you but help improve if possible.
First of all, the board game is just dragging the game back. I like the idea of how it works to move the story forward, and it kinda works, BUT just because something can work, it doesn't mean it is ideal.
I can imagine that if you removed the board game, you could have easily made the same game with just a story and not lost any fun at all.
I am not saying you should ditch it. If I understood your long-term plan correctly, the bigger picture is that the story will be going in different directions depending on what's going on the board, and it sounds like an interesting idea. But in that case, you have to make the board game an enjoyable game by itself.
Right now, it isn't - it is just the "chore".
Its first big problem is that it is very easy to realize that you just have to visit everything - provided you have enough money. There is little choice there other than basic gold management (which I am sure everyone is capable of).
You should add other things to do with gold too. Perhaps buy temporary stat multipliers or gifts for your "teachers" (maybe to increase their affection?). For example, you could buy a card that gives you a bonus on X stat that will be used on a specific audition. Why not even buy the audition cards too?
The second thing is that it is also very obvious that you just have to raise your stats, and it is pretty easy to do so too. And even if it were harder, it would just be "raising your stats." Is there a cap? Or is it just an endless - thus pointless - grind? It wasn't tiring for the current content, but I can't see where this goes if they keep going up linearly.
I'd swap the stats to spendable/reducible things, for example, gold - connections/favors - fame (that would also decrease over time). "Looks" plays the role of "endurance," so I guess you could keep it (but there needs to be some negative for not having it - and you should rely on strategic thought to keep it up rather than just landing on the right square).
The point of them being reducible is that you can create a system where the player gets to spend those resources to buy auditions, audition opportunities, training sessions, or other things. Maybe sth to modify your models' attitude too?
I'd keep the model ability scores dependent but separate from the board game, as, from my understanding, you want them to go up as the story progresses. (And it makes sense too).
You could also do something entirely different, the point is that you want the player to have fun because of the lewds *and* the board game, not have fun *despite* the board game.
Anyway, if you want, I could discuss more ideas with you, but I already feel like I am talking too much, and I think you can understand what I mean.
That being said, I really liked the story so far. It is realistic, and cliche-looking but also not really predictable.